CN109829256B - Cycloidal gear tooth profile straight-line method shaping method, cycloidal gear and speed reducer - Google Patents
Cycloidal gear tooth profile straight-line method shaping method, cycloidal gear and speed reducer Download PDFInfo
- Publication number
- CN109829256B CN109829256B CN201910218900.6A CN201910218900A CN109829256B CN 109829256 B CN109829256 B CN 109829256B CN 201910218900 A CN201910218900 A CN 201910218900A CN 109829256 B CN109829256 B CN 109829256B
- Authority
- CN
- China
- Prior art keywords
- modification
- tooth profile
- point
- cycloidal gear
- pressure angle
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 39
- 239000003638 chemical reducing agent Substances 0.000 title claims abstract description 13
- 238000007493 shaping process Methods 0.000 title claims description 7
- 238000012986 modification Methods 0.000 claims abstract description 215
- 230000004048 modification Effects 0.000 claims abstract description 215
- 238000009826 distribution Methods 0.000 claims abstract description 23
- 238000002715 modification method Methods 0.000 claims abstract description 13
- 230000005540 biological transmission Effects 0.000 claims description 37
- 238000012937 correction Methods 0.000 claims description 8
- 238000012360 testing method Methods 0.000 claims description 7
- 238000012545 processing Methods 0.000 abstract description 5
- 238000009966 trimming Methods 0.000 abstract description 5
- 210000004746 tooth root Anatomy 0.000 description 28
- 238000005461 lubrication Methods 0.000 description 8
- 230000000694 effects Effects 0.000 description 6
- 238000010586 diagram Methods 0.000 description 4
- 230000009286 beneficial effect Effects 0.000 description 3
- 238000004364 calculation method Methods 0.000 description 3
- 239000010687 lubricating oil Substances 0.000 description 3
- 238000004088 simulation Methods 0.000 description 3
- 238000013461 design Methods 0.000 description 2
- 230000008439 repair process Effects 0.000 description 2
- 230000009351 contact transmission Effects 0.000 description 1
- 230000008602 contraction Effects 0.000 description 1
- 230000005489 elastic deformation Effects 0.000 description 1
- 230000002349 favourable effect Effects 0.000 description 1
- 238000010862 gear shaping Methods 0.000 description 1
- 238000009434 installation Methods 0.000 description 1
- 238000003754 machining Methods 0.000 description 1
- 230000007246 mechanism Effects 0.000 description 1
- 230000008569 process Effects 0.000 description 1
- 238000005096 rolling process Methods 0.000 description 1
- 238000012546 transfer Methods 0.000 description 1
Images
Landscapes
- Gears, Cams (AREA)
Abstract
The invention relates to the technical field of processing of a cycloid wheel, in particular to a method for trimming a tooth profile of the cycloid wheel by a straight line method, the cycloid wheel and a speed reducer. The shape modification method comprises the following steps: 1) Determining a distribution rule between pressure angles and meshing phase angles at each point in the tooth profile of the cycloidal gear; 2) Obtaining the minimum point of the pressure angle, the modification quantity of the tooth top and the tooth root; 3) Establishing a first linear equation of the relation between the pressure angle and the modification amount of each tooth profile point in the range from the modification reference point to the tooth top by taking the modification reference point, the pressure angle of the tooth top and the modification amount as two end points; establishing a second linear equation of the relation between the pressure angle and the modification amount of each tooth profile point in the range from the modification reference point to the tooth root by taking the pressure angle and the modification amount of the modification reference point and the tooth root as two end points; 4) Obtaining the modification quantity of each point of the tooth profile of the cycloidal gear according to the first and second linear equations and the distribution rule; 5) And subtracting the respective corresponding modification amount along the normal direction of each tooth profile point of the cycloidal gear to obtain the modified cycloidal gear tooth profile.
Description
Technical Field
The invention relates to the technical field of processing of a cycloid wheel, in particular to a method for trimming a tooth profile of the cycloid wheel by a straight line method, the cycloid wheel and a speed reducer.
Background
The RV reducer is used as an important part of robot transmission, the influence of cycloid pinwheel planetary transmission on the transmission precision is most direct, and the standard cycloid planetary transmission does not have meshing gaps. However, due to the fact that machining and installation errors exist in all parts in the cycloid pin wheel planetary transmission system, elastic deformation can occur after loading, and meanwhile, expansion with heat and contraction with cold are prone to occurring when the cycloid pin wheel planetary transmission system is used.
Therefore, in engineering practice, the tooth profile of the cycloid wheel needs to be modified to form a reasonable tooth gap between the cycloid wheel and the needle teeth, so that the transmission requirement and the lubrication requirement can be met.
Disclosure of Invention
The invention aims to provide a method for modifying the tooth profile of a cycloidal gear by a straight line method, which aims to modify the tooth profile of the cycloidal gear so as to meet the requirements of assembly, lubrication and transmission; the cycloidal gear obtained by the shape modification method is also provided, so that the cycloidal gear meets the requirements of assembly, lubrication and transmission; the speed reducer using the cycloid wheel is further provided, so that a cycloid pin wheel planetary transmission system in the speed reducer meets the requirements of assembly, lubrication and transmission.
In order to achieve the purpose, the technical scheme of the cycloidal gear tooth profile straight-line method shaping method is as follows: a cycloidal gear tooth profile straight-line modification method comprises the following steps: 1) Determining a distribution rule between the tooth profile point pressure angle and the meshing phase angle of the cycloidal gear; 2) Obtaining the minimum pressure angle point, the minimum pressure angle point and the minimum pressure angle point, wherein the minimum pressure angle point is smaller than the minimum pressure angle point; 3) Defining a minimum point of the pressure angle as a modification reference point, establishing a first linear equation of the relationship between the pressure angle and the modification amount of each tooth profile point in a range from the modification reference point to the tooth top by taking the pressure angle and the modification amount of the modification reference point and the pressure angle and the modification amount of the tooth top as two end points, and gradually increasing the modification amount from the modification reference point to each point at the tooth top; establishing a second linear equation of the relationship between the pressure angle and the modification amount of each tooth profile point in the range from the modification reference point to the tooth root by taking the pressure angle and the modification amount of the modification reference point and the pressure angle and the modification amount of the tooth root as two end points, wherein the modification amount from the modification reference point to each point at the tooth root is gradually increased; 4) Obtaining the modification quantity of each point of the tooth profile of the cycloidal gear according to the first and second linear equations in the step 3) and the distribution rule in the step 1); 5) And (3) modifying the tooth profile of the theoretical cycloidal gear, and subtracting the corresponding modification amount along the normal direction of each tooth profile point of the cycloidal gear to obtain the modified cycloidal gear tooth profile.
The invention has the beneficial effects that: according to the straight line method shape modification method provided by the invention, the position of the minimum point of the pressure angle on the tooth profile of the cycloidal gear can be obtained through the distribution rules of the pressure angle and the meshing phase angle, the relation between the pressure angle and the shape modification quantity at each point can be obtained through a first linear equation established by the shape modification reference point and the tooth top and a second linear equation established by the shape modification reference point and the tooth root, and the shape modification quantity and the meshing phase angle can be corresponded by combining the relation between the pressure angle and the meshing phase angle to obtain the shape modification quantity at different points of the cycloidal gear. In the invention, the modification reference point is the minimum point of the pressure angle, the modification amount at the modification reference point is the minimum, the smaller the pressure angle is, the better the force transmission performance is, in the modified cycloid wheel, the part close to the modification reference point is the working section, the force transmission performance is better during meshing, the modification amount is smaller and is close to the conjugate tooth profile, the meshing performance is ensured, the part far away from the modification reference point and close to the tooth top (tooth root) is the non-working section, the modification amount is large, and the non-working section can be ensured to have a reasonable meshing gap so as to store lubricating oil for lubrication.
Further, in the step 1), the distribution rule of the pressure angle and the meshing phase angle satisfies the following equation:
in the formula: alpha is a pressure angle, and alpha is a pressure angle,
is a unit vector of the speed of the cycloid wheel,
is a unit vector of a common normal line,
is the meshing point tangent vector, where x c Is the abscissa, y, of the profile of the cycloidal gear c Is the vertical coordinate of the tooth profile of the cycloidal gear,
is the meshing phase angle.
The effect of this scheme lies in: by establishing a distribution rule of the pressure angle and the meshing phase angle, after the relation between the pressure angle and the modification amount is obtained, the modification amount and the meshing phase angle are in one-to-one correspondence, so that the modification amount of each point corresponds to the tooth profile of the cycloidal gear.
Further, in step 3), the first linear equation is:
the second equation of a straight line is:
wherein, deltaL is a modification amount, alpha is a pressure angle, and alpha is 0 Pressure angle, alpha, being a reference point for shaping tip Is the pressure angle of the tooth tip, α root Is the pressure angle of the tooth root, Δ L 0 For the correction of the correction reference point, Δ L tip Is the amount of addendum modification, Δ L root The root profile modification is the root profile modification.
Further, after the modification amount of each point of the tooth profile is obtained, the modification amount of each point of the tooth profile is superposed on the theoretical tooth profile along the normal direction of the corresponding point, so that the corresponding modification amount is subtracted from the tooth profile of the modified cycloidal gear along the normal direction, and the tooth profile equation of the modified cycloidal gear is as follows:
wherein x is the horizontal coordinate of the tooth profile of the cycloidal gear, y is the vertical coordinate of the tooth profile of the cycloidal gear,
r p the radius of the circle r is distributed for the needle teeth rp The radius of the needle teeth is the radius,
for the phase angle of engagement, a is eccentricity, z c Is the number of teeth of the cycloid gear, z p Is the number of teeth of the pin gear, k 1 Is a short amplitude coefficient.
The cycloidal gear shaping method has the advantages that by establishing the equation of the tooth profile of the trimmed cycloidal gear, the trimmed cycloidal gear can be directly shaped in batch processing, and the trimming does not need to be carried out one by one.
Further, in the step 4), the modification amount of each point of the tooth profile is superposed on the theoretical tooth profile along the normal direction of the corresponding point, so that the modified tooth profile of the cycloidal gear subtracts the corresponding modification amount along the normal direction to obtain the modified tooth profile of the cycloidal gear, and then a test is carried out, and the modification amounts of the modification reference point, the tooth top and the tooth profile are continuously adjusted, so that the modified cycloidal gear meets the required force transmission performance and meshing performance.
The effect of this scheme lies in, for the cycloid wheel after guaranteeing to repair the shape satisfies the requirement of biography power performance and meshing performance, constantly adjusts the volume of repairing the shape of presetting to improve the various performances of cycloid wheel after repairing the shape.
The technical scheme of the cycloid wheel is as follows: a cycloidal gear is obtained by a shape modification method, and the shape modification method comprises the following steps: 1) Determining a distribution rule between the tooth profile point pressure angle and the meshing phase angle of the cycloidal gear; 2) Obtaining the minimum pressure angle point, the minimum pressure angle point and the minimum pressure angle point, wherein the minimum pressure angle point is smaller than the minimum pressure angle point; 3) Defining a minimum point of a pressure angle as a modification reference point, establishing a first linear equation of the relationship between the pressure angle and the modification amount of each tooth profile point in the range from the modification reference point to the tooth top by taking the pressure angle and the modification amount of the modification reference point and the pressure angle and the modification amount of the tooth top as two end points, and gradually increasing the modification amount from the modification reference point to each point at the tooth top; establishing a second linear equation of the relationship between the pressure angle and the modification amount of each tooth profile point in the range from the modification reference point to the tooth root by taking the pressure angle and the modification amount of the modification reference point and the pressure angle and the modification amount of the tooth root as two end points, wherein the modification amount from the modification reference point to each point at the tooth root is gradually increased; 4) Obtaining the modification quantity of each point of the tooth profile of the cycloidal gear according to the first and second linear equations in the step 3) and the distribution rule in the step 1); 5) And (3) modifying the tooth profile of the theoretical cycloidal gear, and subtracting the corresponding modification amount along the normal direction of each tooth profile point of the cycloidal gear to obtain the modified tooth profile of the cycloidal gear.
The beneficial effects of the invention are: the cycloid wheel provided by the invention is obtained by a shape modifying method, in the shape modifying method, the position of the minimum point of the pressure angle on the tooth profile of the cycloid wheel can be obtained through the distribution rules of the pressure angle and the meshing phase angle, the relation between the pressure angle and the shape modifying quantity at each point can be obtained through a first linear equation established by a shape modifying reference point and a tooth top and a second linear equation established by the shape modifying reference point and a tooth root, and the shape modifying quantity and the meshing phase angle can be corresponding by combining the relation between the pressure angle and the meshing phase angle to obtain the shape modifying quantity at different points of the cycloid wheel. In the invention, the modification reference point is the minimum point of the pressure angle, the modification amount at the modification reference point is the minimum, the smaller the pressure angle is, the better the force transmission performance is, in the modified cycloid wheel, the part close to the modification reference point is the working section, the force transmission performance is better during meshing, the modification amount is smaller and is close to the conjugate tooth profile, the meshing performance is ensured, the part far away from the modification reference point and close to the tooth top (tooth root) is the non-working section, the modification amount is large, and the non-working section can be ensured to have a reasonable meshing gap so as to store lubricating oil for lubrication.
Further, in the step 1), the distribution rule of the pressure angle and the meshing phase angle satisfies the following equation:
in the formula: alpha is the pressure angle and alpha is the pressure angle,
is a unit vector of the speed of the cycloid wheel,
is a unit vector of a common normal line,
is the meshing point tangent vector where x c As abscissa, y, of the profile of the cycloidal gear c Is the vertical coordinate of the tooth profile of the cycloidal gear,
is the meshing phase angle.
The effect of this scheme lies in: by establishing a distribution rule of the pressure angle and the meshing phase angle, after the relation between the pressure angle and the modification amount is obtained, the modification amount and the meshing phase angle are in one-to-one correspondence, so that the modification amount of each point corresponds to the tooth profile of the cycloidal gear.
Further, in step 3), the first linear equation is:
the second equation of a straight line is:
wherein, deltaL is the modification amount, alpha is the pressure angle, alpha 0 Pressure angle, alpha, being a reference point for shaping tip Is the pressure angle of the tooth tip, α root Pressure angle of tooth root, Δ L 0 For the correction of the correction reference point, Δ L tip Is the modification of tooth tip, Δ L root The root profile modification is the root profile modification.
Further, after the modification amount of each point of the tooth profile is obtained, the modification amount of each point of the tooth profile is superposed on the theoretical tooth profile along the normal direction of the corresponding point, so that the corresponding modification amount is subtracted from the tooth profile of the modified cycloidal gear along the normal direction, and the tooth profile equation of the modified cycloidal gear is as follows:
wherein x is the horizontal coordinate of the tooth profile of the cycloidal gear, y is the vertical coordinate of the tooth profile of the cycloidal gear,
r p the radius of the circle r is distributed for the needle teeth rp The radius of the needle teeth is the radius,
for the phase angle of engagement, a is eccentricity, z c Is the number of teeth of the cycloid gear, z p Number of pin gear teeth, k 1 Are short-amplitude coefficients.
The method has the advantages that the equation of the tooth profile of the trimmed cycloidal gear is established, the trimmed cycloidal gear can be directly molded in batch processing, and the trimming does not need to be performed one by one.
Further, in the step 4), the modification amount of each point of the tooth profile is superposed on the theoretical tooth profile along the normal direction of the corresponding point, so that the corresponding modification amount is subtracted from the tooth profile of the modified cycloidal gear along the normal direction to obtain the tooth profile of the modified cycloidal gear, and then a test is carried out, and the modification amounts of the modification reference point, the tooth top and the tooth profile are continuously adjusted to ensure that the modified cycloidal gear meets the required force transmission performance and meshing performance.
The effect of this scheme lies in, for guaranteeing that the cycloid wheel after the correction of the shape satisfies the requirement of biography power performance and meshing performance, constantly adjust the shape volume of predetermineeing to improve the various performances of cycloid wheel after the correction of the shape.
The technical scheme of the speed reducer is as follows: a speed reducer comprises a cycloidal pin wheel planetary transmission system, wherein the cycloidal pin wheel planetary transmission system comprises a cycloidal wheel and a pin wheel, the cycloidal wheel is obtained by a cycloidal wheel tooth profile modification method, and the modification method comprises the following steps: 1) Determining a distribution rule between the tooth profile point pressure angle and the meshing phase angle of the cycloidal gear; 2) Obtaining the minimum pressure angle point, the minimum pressure angle point and the minimum pressure angle point, wherein the minimum pressure angle point is smaller than the minimum pressure angle point; 3) Defining a minimum point of a pressure angle as a modification reference point, establishing a first linear equation of the relationship between the pressure angle and the modification amount of each tooth profile point in the range from the modification reference point to the tooth top by taking the pressure angle and the modification amount of the modification reference point and the pressure angle and the modification amount of the tooth top as two end points, and gradually increasing the modification amount from the modification reference point to each point at the tooth top; establishing a second linear equation of the relationship between the pressure angle and the modification amount of each tooth profile point in the range from the modification reference point to the tooth root by taking the pressure angle and the modification amount of the modification reference point and the pressure angle and the modification amount of the tooth root as two end points, wherein the modification amount from the modification reference point to each point at the tooth root is gradually increased; 4) Obtaining the modification quantity of each point of the tooth profile of the cycloidal gear according to the first and second linear equations in the step 3) and the distribution rule in the step 1); 5) And (3) modifying the tooth profile of the theoretical cycloidal gear, and subtracting the corresponding modification amount along the normal direction of each tooth profile point of the cycloidal gear to obtain the modified cycloidal gear tooth profile.
The invention has the beneficial effects that: the cycloid wheel in the speed reducer is obtained by a shape modifying method, in the shape modifying method, the position of the minimum point of the pressure angle on the tooth profile of the cycloid wheel can be obtained through the distribution rule of the pressure angle and the meshing phase angle, the relation between the pressure angle and the shape modifying quantity at each point can be obtained through a first linear equation established by a shape modifying reference point and a tooth crest and a second linear equation established by the shape modifying reference point and a tooth root, and the shape modifying quantity and the meshing phase angle can be corresponding by combining the relation between the pressure angle and the meshing phase angle to obtain the shape modifying quantity at different points of the cycloid wheel. In the invention, the modification reference point is the minimum point of the pressure angle, the modification amount at the modification reference point is the minimum, the smaller the pressure angle is, the better the force transmission performance is, in the modified cycloid wheel, the part close to the modification reference point is the working section, the force transmission performance is better during meshing, the modification amount is smaller and is close to the conjugate tooth profile, the meshing performance is ensured, the part far away from the modification reference point and close to the tooth top (tooth root) is the non-working section, the modification amount is large, and the non-working section can be ensured to have a reasonable meshing gap so as to store lubricating oil for lubrication.
Further, in the step 1), the distribution rule of the pressure angle and the meshing phase angle satisfies the following equation:
in the formula: alpha is the pressure angle and alpha is the pressure angle,
is a unit vector of the speed of the cycloid wheel,
is a unit vector of a common normal line,
is the meshing point tangent vector, where x c Is the abscissa, y, of the profile of the cycloidal gear c Is the vertical coordinate of the tooth profile of the cycloidal gear,
is the phase angle of the engagement.
The effect of this scheme lies in: by establishing a distribution rule of the pressure angle and the meshing phase angle, after the relation between the pressure angle and the modification amount is obtained, the modification amount and the meshing phase angle are in one-to-one correspondence, so that the modification amount of each point corresponds to the tooth profile of the cycloidal gear.
Further, in step 3), the first linear equation is:
the second equation of a straight line is:
wherein, deltaL is the modification amount, alpha is the pressure angle, alpha 0 Pressure angle, alpha, being a reference point for shaping tip Is the pressure angle of the tooth crest, alpha root Pressure angle of tooth root, Δ L 0 For the modification of the modification reference point, Δ L tip Is the modification of tooth tip, Δ L root Is a toothRoot modification amount.
Further, after the modification quantity of each tooth profile point is obtained, the modification quantity of each tooth profile point is superposed on the theoretical tooth profile along the normal direction of the corresponding point, so that the corresponding modification quantity is subtracted from the modified cycloidal gear tooth profile along the normal direction, and the cycloidal gear tooth profile equation after modification is as follows:
wherein x is the abscissa of the tooth profile of the cycloidal gear, y is the ordinate of the tooth profile of the cycloidal gear,
r p the radius of the circle r is distributed for the needle teeth rp Is the radius of the needle teeth, and the needle teeth,
for the phase angle of engagement, a is eccentricity, z c Is the number of teeth of the cycloid gear, z p Is the number of teeth of the pin gear, k 1 Is a short amplitude coefficient.
The method has the advantages that the equation of the tooth profile of the trimmed cycloidal gear is established, the trimmed cycloidal gear can be directly molded in batch processing, and the trimming does not need to be performed one by one.
Further, in the step 4), the modification amount of each point of the tooth profile is superposed on the theoretical tooth profile along the normal direction of the corresponding point, so that the modified tooth profile of the cycloidal gear subtracts the corresponding modification amount along the normal direction to obtain the modified tooth profile of the cycloidal gear, and then a test is carried out, and the modification amounts of the modification reference point, the tooth top and the tooth profile are continuously adjusted, so that the modified cycloidal gear meets the required force transmission performance and meshing performance.
The effect of this scheme lies in, for the cycloid wheel after guaranteeing to repair the shape satisfies the requirement of biography power performance and meshing performance, constantly adjusts the volume of repairing the shape of presetting to improve the various performances of cycloid wheel after repairing the shape.
Drawings
FIG. 1 is a schematic view showing the meshing state of a cycloid wheel and needle teeth in a cycloid pin gear planetary transmission system in an embodiment of a method for straight-line modification of a cycloid wheel tooth profile according to the present invention;
FIG. 2 is a graph showing the correspondence between the meshing phase angle and the pressure angle in embodiment 1 of the method for modifying the tooth profile of a cycloid gear of the present invention;
FIG. 3 is a schematic view of a cycloid wheel tooth profile after the corresponding relationship of the meshing phase angle and the pressure angle is embodied on the cycloid wheel tooth profile in embodiment 1 of the method for modifying the cycloid wheel tooth profile of the present invention;
FIG. 4 is a schematic diagram illustrating the influence of the pressure angle on the transmission performance in the embodiment of the method for straight-line modification of the cycloid wheel tooth profile according to the invention;
FIG. 5 is a schematic diagram showing a comparison between a theoretical tooth profile and a modified designed tooth profile in an embodiment of a method for modifying the tooth profile of a cycloidal gear according to the invention by a straight-line method;
FIG. 6 is a schematic diagram illustrating a distribution trend of a modification amount of a tooth profile section from a modification reference point to a tooth root in an embodiment of a straight-line modification method of a cycloid gear tooth profile according to the present invention;
FIG. 7 is a schematic view showing a distribution trend of the modification amount of the tooth profile section from the modification reference point to the tooth crest in the embodiment of the method for modifying the tooth profile of the cycloidal gear by the straight-line method.
Detailed Description
Embodiments of the present invention will be further described with reference to the accompanying drawings.
The embodiment of the method for modifying the profile of the cycloidal gear by the straight line method is shown in fig. 1 to 7, and the embodiment determines the modification amount of each point in the profile of the cycloidal gear by using the optimal force transmission performance as the principle of the modification amount calculation, subtracts the respective corresponding modification amount along the normal direction of the corresponding point to obtain the modified profile of the cycloidal gear, and performs a simulation test to adjust the modification amount.
The method specifically comprises the following steps:
1. determining distribution rule of tooth profile point pressure angle and meshing phase angle of cycloidal gear
Establishing a schematic view of the meshing state of the cycloid wheel and the pin gear as shown in FIG. 1, wherein O f Is the origin of the pin wheel coordinate system, O c Is the origin of the cycloidal gear coordinate system r a Is the base radius, r b Is the radius of the rolling circle, P is the node, K is the meshing point, M is the needleThe center of the tooth is positioned at the center of the tooth,
is a unit vector of the speed of the cycloid wheel,
is a common normal unit vector and alpha is a pressure angle.
The pressure angle is defined as the angle between the direction of the force applied to the driven member and the direction of the speed of the point of application of the force when the mechanism is in motion, without taking into account the frictional forces. According to the motion principle of planetary transmission of cycloid pin gears, the pressure angle alpha is the unit vector of the common normal line of the meshing point of the tooth profile of the cycloid gear and the tooth profile of the pin gear
Unit vector of speed with cycloid wheel
The included angle of (c). As can be seen from FIG. 1, the common normal unit vector at the meshing point K
Unit vector of speed with cycloid wheel
Satisfies the following formula:
in the formula (1-1), the unit vector of the speed of the cycloid wheel is:
in the formula (1-1), the common normal unit vector of the tooth profile meshing point:
in the formulae (1-2) and (1-3),
is the meshing point tangent vector, where x c As abscissa, y, of the profile of the cycloidal gear c Is the vertical coordinate of the tooth profile of the cycloidal gear,
is a unit normal vector of the x-axis direction,
is a unit normal vector of the y-axis direction,
is the phase angle of the engagement.
In conclusion, the formula of the tooth profile pressure angle of the cycloid wheel can be obtained:
from this, the pressure angle α and the engagement phase angle can be determined
Due to the phase angle of engagement of each point in the cycloidal gear tooth profile
For a determined value, the pressure angle of each point in the profile of the cycloidal gear can thus be derived.
Fig. 2 and 3 can be derived from the equations (1-4), fig. 2 shows the correspondence between the meshing phase angle and the pressure angle, and fig. 3 is a view obtained by expressing the correspondence on the cycloid gear tooth profile.
As can be seen from FIGS. 2 and 3, the phase angle of engagement is
And
has a minimum pressure angle of alpha 0 . While the pressure angle at the tooth tip and root is maximum, 90 °. As can be seen in fig. 4, the effective force component F n The calculation formula of (2) is as follows: f n = Fcos α, where F is the resultant force, and the smaller the pressure angle α, the effective component force F n The larger the size, the better the force transfer performance.
In the embodiment, the range of the tooth profile working section of the cycloidal gear is determined on the principle of optimal force transmission performance, and the pressure angle of an engagement point when the cycloidal-pin gear planetary transmission system is engaged is assumed to be alpha 1 The pressure angle of the engagement point at the time of disengagement is alpha 2 Thus, the pressure angle α 1 And pressure angle alpha 2 The corresponding cycloidal gear tooth profile section is the cycloidal gear tooth profile working section.
2. Obtaining the minimum point of the pressure angle, the modification amount of the tooth top and the tooth root
As can be seen from fig. 2 and 3, the pressure angle at the minimum point of the pressure angle is α 0 Where the effective component is greatest at engagement, and alpha 1 And alpha 2 With respect to alpha 0 The symmetrical arrangement is more favorable for the symmetry of a gear tooth contact transmission error curve, and the good force transmission performance is ensured.
Wherein the minimum point of the pressure angle, the modification amount of the tooth top and the tooth root are preset according to experience when selecting, and the minimum point alpha of the pressure angle is preset 0 Has a modification amount of DeltaL 0 (ii) a The pressure angle of the tooth crest is alpha tip The modification amount of the tooth top is DeltaL tip (ii) a The pressure angle of the tooth root being alpha root Root of tooth is modified by Δ L root . Wherein, Δ L 0 Less than Δ L tip While Δ L 0 Less than Δ L root . And defining the minimum point of the pressure angle as a modification reference point.
3. Establishing a first linear equation from the modification reference point to the tooth top and a second linear equation from the modification reference point to the tooth bottom
In the present embodiment, as shown in fig. 7, the pressure angle α is represented by the x-axis, and the modification amount Δ L is represented by the y-axis.
Parameter (alpha) of reference point to be shaped 0 ,ΔL 0 ) Parameter of addendum modification reference point (alpha) tip ,ΔL tip ) As two end points of the linear equation, a linear modification quantity equation (i.e., a first linear equation) from the modification reference point to the tooth crest can be obtained:
as shown in fig. 6, the pressure angle α is represented by the x-axis, and the modification amount Δ L is represented by the y-axis. Parameter (alpha) of reference point to be shaped 0 ,ΔL 0 ) Parameter of addendum modification reference point (alpha) root ,ΔL root ) As two end points of the linear equation, a linear shape modification quantity equation (i.e., a second linear equation) from the shape modification reference point to the tooth root can be obtained:
in the formulas (3-1) and (3-2), deltaL is a modification amount, and alpha is a pressure angle.
4. Determining modification quantity of each point of cycloidal gear tooth profile
According to the formulas (3-1) and (3-2), the modification amount corresponding to each pressure angle in the cycloidal gear tooth profile can be calculated, then the modification amount corresponding to each meshing phase angle in the cycloidal gear tooth profile can be obtained according to the formulas (1-4), in actual operation, different points in the cycloidal gear tooth profile correspond to different meshing phase angles, the positions of the corresponding points can be obtained through the numerical values of the meshing phase angles, then the modification amount of the corresponding points can be obtained through the formulas (1-4), (3-1) and (3-2), and the schematic diagram shown in fig. 5 can be obtained. The shape-modified design tooth profile of the cycloidal gear is obtained, and as can be seen from fig. 5, the modification amount of the working section close to the modification reference point is small, the working section is close to the conjugate tooth profile as much as possible, so that the meshing performance and the force transmission performance are ensured, the modification amount of the non-working section close to the tooth top and the tooth root is large, the reasonable meshing clearance can be ensured, and the performances such as lubrication and the like are ensured.
5. Obtaining the tooth profile equation of the modified cycloidal gear according to the tooth profile modification quantity equation
On the basis of the cycloid equation of the tooth profile of a theoretical cycloidal gear (or called as a standard cycloidal gear), the modification quantities are effectively superposed along the normal direction of each tooth profile point, and the modification quantities are subtracted from the tooth profile of the theoretical cycloidal gear, so that the following cycloidal gear tooth profile equation can be obtained:
wherein, the formula of the modification amount Δ L in the formula (5-1) is different between the formula of the tooth profile section from the modification reference point to the tooth crest and the formula of the tooth profile section from the modification reference point to the tooth root, and the modification amount of the tooth profile section from the modification reference point to the tooth crest satisfies the following formula:
and the modification amount of the tooth profile section from the modification reference point to the tooth root satisfies the following formula:
in the formula (5-1), x is the horizontal coordinate of the tooth profile of the cycloidal gear, y is the vertical coordinate of the tooth profile of the cycloidal gear,
r p the radius of the circle r is distributed for the needle teeth rp The radius of the needle teeth is the radius,
for the phase angle of engagement, a is eccentricity, z c Is the number of teeth of the cycloid gear, z p Is the number of teeth of the pin gear, k 1 Are short-amplitude coefficients.
In the formulas (5-2) and (5-3), alpha is a pressure angle and alpha 0 Pressure angle, Δ L, of a reference point for profiling tip Is the addendum modification amount, Δ L root For root relief, Δ L 0 Is the modification amount of the reference point.
In this embodiment, in the step (ii), the modification reference points, the tooth tops and the tooth roots are preset values, and in the actual design, after the modification values are superimposed on the theoretical tooth profile, an analog simulation is performed, and the three modification values are adjusted with the force transmission performance and the meshing performance as targets until the tooth profile of the cycloidal gear is modified to meet the required tooth profile. In other embodiments, after the simulation, if the profile of the modified cycloid gear meets the use requirement, the adjustment can be not continued. In other embodiments, if the actual cost is not considered and a more real use environment is pursued, the actual shape modification can be performed on the tooth profile of the cycloidal gear, then the actual test is performed, the transmission performance and the meshing performance are detected in the test process, and then the shape modification amount is adjusted.
In this embodiment, for the convenience of calculation, the modification amount of the modification reference point may be preset to zero.
In the embodiment of the cycloid wheel of the invention, the cycloid wheel is obtained by a shape modification method, and the shape modification method is the same as that in the embodiment.
In a specific embodiment of the reducer of the present invention, the reducer comprises a cycloidal pin gear planetary transmission system, the cycloidal pin gear planetary transmission system comprises a cycloidal gear and pin gears, and the cycloidal gear is the same as that in the above-described embodiment.
Claims (7)
1. A method for modifying the tooth profile of a cycloidal gear by a straight line method is characterized in that: the method comprises the following steps: 1) Determining a distribution rule between the tooth profile point pressure angle and the meshing phase angle of the cycloidal gear; 2) Obtaining the minimum pressure angle point, the minimum pressure angle point and the minimum pressure angle point, wherein the minimum pressure angle point is smaller than the minimum pressure angle point; 3) Defining a minimum point of a pressure angle as a modification reference point, establishing a first linear equation of the relationship between the pressure angle and the modification amount of each tooth profile point in the range from the modification reference point to the tooth top by taking the pressure angle and the modification amount of the modification reference point and the pressure angle and the modification amount of the tooth top as two end points, and gradually increasing the modification amount from the modification reference point to each point at the tooth top; establishing a second linear equation of the relationship between the pressure angle and the modification amount of each tooth profile point in the range from the modification reference point to the tooth root by taking the pressure angle and the modification amount of the modification reference point and the pressure angle and the modification amount of the tooth root as two end points, wherein the modification amount from the modification reference point to each point at the tooth root is gradually increased; 4) Obtaining the modification quantity of each point of the tooth profile of the cycloidal gear according to the first and second linear equations in the step 3) and the distribution rule in the step 1); 5) And (3) modifying the tooth profile of the theoretical cycloidal gear, and subtracting the corresponding modification amount along the normal direction of each tooth profile point of the cycloidal gear to obtain the modified tooth profile of the cycloidal gear.
2. The method for straight-line modification of the tooth profile of the cycloidal gear according to claim 1, wherein: in the step 1), the distribution rule of the pressure angle and the meshing phase angle meets the following equation:
in the formula: alpha is the pressure angle and alpha is the pressure angle,
is a unit vector of the speed of the cycloid wheel,
is a unit vector of a common normal line,
is the meshing point tangent vector where x c As abscissa, y, of the profile of the cycloidal gear c Is the vertical coordinate of the tooth profile of the cycloidal gear,
is the phase angle of the engagement.
3. The method for straight-line modification of the tooth profile of the cycloidal gear according to claim 1 or 2, wherein: in step 3), the first linear equation is:
the second equation of a straight line is:
wherein, deltaL is a modification amount, alpha is a pressure angle, and alpha is 0 Pressure angle, alpha, being a reference point for shaping tip Is the pressure angle of the tooth crest, alpha root Is the pressure angle of the tooth root, Δ L 0 For the correction of the correction reference point, Δ L tip Is the amount of addendum modification, Δ L root The root modification.
4. The method for straight-line modification of the tooth profile of the cycloidal gear according to claim 3, wherein: after the modification quantity of each point of the tooth profile is obtained, the modification quantity of each point of the tooth profile is superposed on the theoretical tooth profile along the normal direction of the corresponding point, so that the tooth profile of the modified cycloidal gear subtracts the corresponding modification quantity along the normal direction, and the tooth profile equation of the modified cycloidal gear is as follows:
wherein x is the abscissa of the tooth profile of the cycloidal gear, y is the ordinate of the tooth profile of the cycloidal gear,
r p the needle teeth are distributed with a radius r rp Is the radius of the needle teeth, and the needle teeth,
for the phase angle of engagement, a is eccentricity, z c Is the number of teeth of the cycloid gear, z p Number of pin gear teeth, k 1 Are short-amplitude coefficients.
5. The method for straight-line modification of the tooth profile of the cycloidal gear according to claim 1 or 2, wherein: in the step 4), the modification amount of each point of the tooth profile is superposed on the theoretical tooth profile along the normal direction of the corresponding point, so that the corresponding modification amount is subtracted from the modified cycloidal gear tooth profile along the normal direction to obtain the modified cycloidal gear tooth profile, and then a test is carried out, and the modification amounts of the modification reference point, the tooth top and the tooth profile are continuously adjusted, so that the modified cycloidal gear meets the required force transmission performance and meshing performance.
6. A cycloidal gear, comprising: the cycloidal gear is obtained by the cycloidal gear tooth profile straight-line modification method of any one of claims 1 to 5.
7. The utility model provides a speed reducer, includes cycloid pin wheel planetary transmission system, cycloid pin wheel planetary transmission system includes cycloid wheel and pin wheel, its characterized in that: the cycloidal gear is obtained by the cycloidal gear tooth profile straight-line modification method of any one of claims 1-5.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910218900.6A CN109829256B (en) | 2019-03-21 | 2019-03-21 | Cycloidal gear tooth profile straight-line method shaping method, cycloidal gear and speed reducer |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910218900.6A CN109829256B (en) | 2019-03-21 | 2019-03-21 | Cycloidal gear tooth profile straight-line method shaping method, cycloidal gear and speed reducer |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109829256A CN109829256A (en) | 2019-05-31 |
| CN109829256B true CN109829256B (en) | 2022-10-04 |
Family
ID=66870564
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910218900.6A Active CN109829256B (en) | 2019-03-21 | 2019-03-21 | Cycloidal gear tooth profile straight-line method shaping method, cycloidal gear and speed reducer |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109829256B (en) |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2008011764A1 (en) * | 2006-07-21 | 2008-01-31 | Hong Jiang | A kind of gear pair for power transmission in speed increaser or reducer and its forming method |
| CN107229836A (en) * | 2017-07-04 | 2017-10-03 | 河南科技大学 | Cycloid tooth profile correction method and Cycloidal Wheel, RV decelerators |
| CN109307054A (en) * | 2018-01-23 | 2019-02-05 | 华南理工大学 | A kind of segmentation correction method of RV Key Part of Cycloid Cam Planetary Speed Reducer and its flank profil |
-
2019
- 2019-03-21 CN CN201910218900.6A patent/CN109829256B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2008011764A1 (en) * | 2006-07-21 | 2008-01-31 | Hong Jiang | A kind of gear pair for power transmission in speed increaser or reducer and its forming method |
| CN107229836A (en) * | 2017-07-04 | 2017-10-03 | 河南科技大学 | Cycloid tooth profile correction method and Cycloidal Wheel, RV decelerators |
| CN109307054A (en) * | 2018-01-23 | 2019-02-05 | 华南理工大学 | A kind of segmentation correction method of RV Key Part of Cycloid Cam Planetary Speed Reducer and its flank profil |
Non-Patent Citations (2)
| Title |
|---|
| 考虑尺寸公差的摆线齿廓修形方法;刘亭亭等;《机械设计》;20180620(第06期);全文 * |
| 高精度RV减速器摆线轮修形理论研究;柯庆勋等;《机械传动》;20180715(第07期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN109829256A (en) | 2019-05-31 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| US20140256223A1 (en) | Machining Method for Hard-Fine Machining of Noise-Optimized Gears on a Gear-Cutting Machine | |
| CN108953550B (en) | Design method for point tooth surface of straight gear | |
| CN107229836A (en) | Cycloid tooth profile correction method and Cycloidal Wheel, RV decelerators | |
| CN108343725B (en) | Cycloidal gear tooth profile shaping method based on logarithm, cycloidal gear and RV reducer | |
| CN107081678B (en) | Method for dressing grinding wheel for forming and grinding cycloid wheel | |
| CN101389429A (en) | Sintered gear element featuring locally selective surface compression | |
| CN108730480B (en) | Cycloidal gear of RV reducer and tooth profile reverse active modification method thereof | |
| CN101466489A (en) | Work piece having different qualities | |
| CN106392200A (en) | Composite shape correction method for tooth contour of cycloidal gear of RV reducer | |
| CN109902437B (en) | Method for modifying tooth profile of cycloidal gear, cycloidal gear and speed reducer | |
| CN101193716A (en) | Surface-densified toothed section from a sintered material and having special tolerances | |
| CN101193717B (en) | Hardness and roughness of a toothed section from a surface-densified sintered material | |
| CN109829256B (en) | Cycloidal gear tooth profile straight-line method shaping method, cycloidal gear and speed reducer | |
| CN109780167B (en) | Cycloidal gear tooth profile catenary modification method, cycloidal gear and speed reducer | |
| CN109396567B (en) | Digital envelope method for determining profile of worm grinding wheel in generating grinding of shape-modified cycloid gear | |
| Ligata et al. | Geometry definition and contact analysis of spherical involute straight bevel gears | |
| Zhang et al. | Study on Empirical Gear Profile Micro-Modifications for Gear Transmission | |
| CN112035968A (en) | Method for matching and modifying cycloid tooth profile of precise speed reducer for robot | |
| CN108253115B (en) | A method of the form of cycloidal gear tooth is obtained based on pinwheel tooth profiling quantity | |
| Kissling et al. | Face gears: Geometry and strength | |
| CN116467843A (en) | Cycloidal tooth profile secondary conjugate modification method of RV reducer | |
| JP3693466B2 (en) | Molded gear and method for determining tooth profile of molded gear | |
| Liang et al. | Theoretical and experimental investigations on parallel-axis gear transmission with tubular meshing surfaces | |
| CN114861342A (en) | Polynomial and equidistant displacement combined cycloid tooth profile composite modification method | |
| CN109434218B (en) | RU and YU tooth type automobile synchronous belt pulley cutter and design method thereof |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| TR01 | Transfer of patent right | ||
| TR01 | Transfer of patent right |
Effective date of registration: 20240506 Address after: No. 2 Xingye Third Road, Advanced Manufacturing Cluster Zone, Jianxi District, Luoyang City, Henan Province, 471003 Patentee after: Luoyang kedager Transmission Research Institute Co.,Ltd. Country or region after: China Address before: 471003 No. 48, Xiyuan Road, Jianxi District, Henan, Luoyang Patentee before: HENAN University OF SCIENCE AND TECHNOLOGY Country or region before: China |